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Xo = 60 m/s. Yo = 49 m/s. Vo = 60 + 49i = 77.5m/s[39.2o]. A. Y = Yo + g*Tr = 0. 49 + (-9.8)Tr = 0, Tr = 5 s. = Rise time. Tf = Tr = 5 s. = Fall time. Tr+Tf = 5+5 = 10 s. = Time in air. B. d = Xo*(Tr+Tf) = 60*10 = 600 m.
1. M1 = 601 kg, V1 = 0. M2 = 1880 kg, V2 = 14.5 m/s. M1*V1+M2*V2 = M1*V3+M2*V4. 601*0+1880*14.5 = 601*V3+1880*V4, Eq1: 601V3+1880V4 = 27,260, V3 = ((M1-M2)V1 + 2M2*V2)/(M1+M2). V3 = ((601-1880)0 + 3760*14.5)/(601+1880) = 54,520/2481 = 22 m/s. In Eq1,
T1 = d1/V1 = 200/44 = 4.55 h. T2 = 9-4.55 = 4.45 h. V2 = d2/T2 = 220/4.45 = 49.44 km/h.
a. Fr = 453N.[8o] + 400N.[35o]. Fr = x+yi = (453*Cos8+ 400*Cos35) + (453*sin8+400*sin35)I. Fr = 776.3 + 292.5i = 829.6N.[20.6o]. b. Fr = M*a. a = Fr/M = 829.6[20.6]/3805 = 0.218m/s^2[20.6o].
B. d1 = 40*T1 = 100. T1 = 2.5 h. d2 = 60*T2 = 100. T2 = 1.7 h, Vavg. = (d1+d2)/(T1+T2) = 200/4.2 = 47.6 km/h.
A. d = 40*2 + 60*2 = 200 km. Vavg = 200/4 = 50 km/h.
Vo = 55km/h = 55,000m/3600s = 15.3 m/s. d = Vo*T = 15.3*0.75 =
M*g = 13*9.8 = 127.4 N. = Wt. of box. Fp = 127.4*sin55 = 104.4 N. = Force parallel with ramp. Fki = u*Fn = 0.3*127.4*Cos55 = 21.9 N. = Force of kinetic friction. Fe = 160 N. = Force exerted. A. Fp-Fki+Fe = M*a. 104.4-21.9+160 = 13*a, 13a = 242.5, a = 18.7
M*g = 25 * 9.8 = 245 N. Fp = 245*sinA. Fn = 245*CosA. Fs = u*Fn = 0.37 * 245*CosA = 90.7*CosA. = Force of static friction. Fki = u*Fn = 0.24*245*CosA = 58.8*CosA. = Force of kinetic friction. A. Fp-Fs = M*a. 245*sinA-90.7*CosA = 25*0. 245*sinA/CosA-90.7 =
All angles are measured CW from +y-axis. Vpa = 180[203o] + 50[60o]. Vpa = x+yi = (180*sin203+50*sin60) + (180*Cos203+50Cos60)i. Vpa = -27 - 140.7i = 143mph[11o] W. 0f S. = 143mph[191o] CW. TanA = x/y.
Beatty has $(X - 14.20). Amy has $(x+24.80) + 14.20. (x+24.80) + 14.20 = 3(x-14.20). x + 39 = 3x - 42.60 X = $40,80 = Amt. Beatty had at first.
Po = 5445 - 1058 = $4387. P = 132.24 * 48 = $6347.52. T = 48mo. = 4 yrs. P = Po + Po*r*T = 6347.52. 4387 + 4387*r*4 = 6347.52, 4387 + 17,548r = 6347.52, r = 0.112 = 11.2%.
y = 15x. y = total earnings,
y = 2500x.
r = 15/4 = 3,75. r = 9/4 = 2.25. So 9/4 is lower.
50 - 8 = 42 numbers > 8. p = 42/50 = 21/25.
What is your question?
a. 4.1/(7/10) = 4.1 * 10/7 = 5 6/7 or 5 strips. b. 6/7 * 7/10 =
F = M*a = 300 * 0.5[25o] = 150N,[25o] N. of E.
1st = 9.33 - 1.32 = 8.01 sec.
a. h = 0.5*g*T^2 = 52. 4.9*T^2 = 52, T = 1.47 s. b. V^2 = Vo^2 + 2g*d = 0 +29.6*52 = 1539, V = 39. m/s. c. Vx = 18 m/s. d. Vt = sqrt(18^2 + 39^2) =
h = 0.5*g*T^2 = 8.9, 5T^2 = 8.9, T = 1.33 s. Vx * T = 3. Vx * 1.33 = 3, Vx =
16 - 10 1/4 + 7 1/2 = 64/4 - 41/4 + 30/4 = 53/4 = 13 1/4 Pts.
r = (2-10)/4 = -8/4 = -2Ft/h. The water decreased at a rate of 2 ft. per hour. 92-1
I = P*r*T = 375*0.04*5 = $75. Ans.: B,C, and D.
P = Po + Po*r*T. P1 = 10,500 + 10,500*(0.12/360)*40 - 3000 = 10,640 - 3000 = $7,640. P2 = 7,640 + 7640*(0.12/360)*80 = 7843.73 - 2000 = $5843.73. = Bal. after 120 days. P3 = 5843.73 + 5843.73*(0.12/360)*50 = Final amt. due.
-3 < -x-2 < 4. Add 2 to all sides and get: -1 < -x < 6, Multiply all sides by -1 and get: 1 > X > -6. Reversed inequality signs.
C = 2000 + 1.25*2000 =
144/36 = 4 sq. Ft./blk. L*W = 4. L*L = 4, L^2 = 4 L = 2 Ft.
h = 0.5*g*T^2 = 1.5. 4.9T^2 = 1.5, T = Vx*T = 2.6. Vx = 2.6/T.
(-4, 0).
d = Vo^2*sin(2A)/g = 30. Vo^2*sin70/9.8 = 30, Vo^2 * 0.0959 = 30, Vo = 17.7 m/s.
Correct: F = M*a. a = F/M.
(-5, -1), (10, -7). Y = mx + b. m = (-7+1)/(10+5) = -6/15 = -2/5. b = y-mx = -1-(-2/5(-5) = -1 - 2 = -3. Y = -2x/5 - 3. 2x/5 + y = -3, 2x + 5y = -15.
sqrt(12x^20y^8) = sqrt(3*4x^20y^8) = sqrt(3)*2x^10 y^4.
e. Fnet = Fe-Fp+uFn = 414-1348+934 = 0. Wnet = Fnet * d = 0 * 4.2 = 0.
Correction: Fex-Fp+Fk = M*a. Repeat all calculations.
a. M*g = 275*9.8 = 2695 N. = Wt. of piano. Fp = 2695*sin30 = 1348 N. = Force parallel with plane. Fn = 2695*Cos30 = 2334 N. = Normal force. u*Fn = 0.4*2334 = 934 N. = Force of kinetic friction. Fe-Fp+u*Fn = M*a. Fe-1348+934 = M*0, Fe - 414 = 0, Fe = 414 N.
25*Cos A = 12. A =
D^2 = S1^2 + S2^2.
Correction: c^2 = S1^2 + S2^2.
c^2 = s^2 + s^2 = 2s^2.
d = Vo^2*sin(2A)/g = 3.34 m. Vo^2*sin53.4/9.81 = 3.34, Vo^2*0.082 = 3.34, Vo = 6.4 m/s.
19x + 28x = 90. X = 1.915. 19x = 36.38o. 28x = 53.62o.
Tan A = h/d. Tan32 = 56/d, d =
X cars. 3x lorries.. 30*x + 42*3x = 1092. X = 3x = x + 3x = total cars.
h = 0.5*g*T^2 = 147. T = d = Vx*T. d = 44*T.
d1 = V1*T = 650[40o] * 1.5 = 975 m.[40o]. d2 = V2*T = 560[108o] * 1.5 = 840 m[108o]. d = d1-d2, d = 975[40o] - 840[108o]. X = 975*Cos40 - 840*Cos108 = Y = 975*sin40 - 840*sin108 = d = sqrt(x^2 + y^2).
V^2 = Vo^2 + 2g*h. = 0 + 19.6*130 = 2548, V =
40o S. of E. = 320o CCW. d = 17km[320o]. X = 17*Cos320 = East component. Y = 17*sin320 = South component. No north component.
